scholarly journals Refraction and reflection of an obliquely incident finite amplitude plane P wave at a plane solid—solid interface

1989 ◽  
Vol 85 (S1) ◽  
pp. S139-S139
Author(s):  
Kun‐Tien Shu ◽  
Jerry H. Ginsberg
Keyword(s):  
Finite Amplitude ◽  
P Wave ◽  
Solid Interface ◽  
Obliquely Incident ◽  
Plane P Wave

Rise times of attenuated seismic pulses detected in both empty and fluid‐filled cylindrical boreholes

Geophysics ◽  
1984 ◽  
Vol 49 (4) ◽  
pp. 398-410 ◽  
Author(s):  
D. P. Blair
Keyword(s):  
Stress Wave ◽  
Particle Motion ◽  
P Wave ◽  
Wave Incident ◽  
Stress Wave Propagation ◽  
Linear Phase ◽  
Phase Filter ◽  
Mathematical Expressions ◽  
Plane P Wave ◽  
Theory And Experiment

Fourier‐Bessel theory is used to derive filters representing the influence of both empty and fluid‐filled cylindrical boreholes on particle motion induced in rock by a plane P-wave incident perpendicular to the borehole axis. For wavelengths greater than 10 times the borehole circumference, the effect of the borehole on particle motions is shown to be negligible; thus the results have little relevance for the long wavelengths commonly encountered in earthquake seismology. The results are, however, relevant to the study of stress wave propagation at ultrasonic frequencies in rock masses. For small wavelengths (αa > 3.0) the filter representing particle motion on the wave incident site of an empty borehole reduces to a linear phase filter which increases all amplitudes by a factor of 2 while the filter representing fluid stress at the center of a fluid‐filled borehole may be reduced to simple mathematical expressions. Experimental results were obtained for the interaction of a stress wave with either accelerometers mounted in an empty borehole or a hydrophone located centrally in a fluid‐filled borehole. Both theory and experiment show a similar distortion in the rise time of the pulse traveling past the borehole.

ANALYSIS AND PROCESSING OF RECEIVED SIGNALS IN BOREHOLES

2001 ◽  
Vol 09 (02) ◽  
pp. 447-459 ◽  
Author(s):  
JENS M. HOVEM ◽  
HEFENG DONG ◽  
ODDVAR LOTSBERG
Keyword(s):  
Geological Structure ◽  
P Wave ◽  
Resonance Structure ◽  
Time Of Arrival ◽  
Reflected Waves ◽  
Sensor Signals ◽  
The Individual ◽  
Spatial And Temporal Characteristics ◽  
Plane P Wave

This study is a part of a project to develop a borehole sonar for acoustic imaging of the geological structure of the rock formation near to a deviated or horizontal borehole performed while drilling. The purpose of the sonar is to provide a direct measure of the distance and the direction to bed boundaries parallel to the borehole. This paper gives a theoretical analysis of the effect of the borehole and the drillstring on the received response on sensors positioned on the drillstring and proposes a method for processing the received signal to enable the determination of the direction of an incoming plane wave and time of arrival. In the first part of this paper, the response at any position in a fluid filled borehole is determined for an incoming plane P-wave. It is shown that the response is quite complicated and consists of several vibrating modes with resonance structure. Secondly, the paper presents how the received signals can be decomposed and the individual modes can be resolved by utilizing the orthogonal properties of the mode functions. The individual mode functions are resolved by performing a spatial Fourier transform of the sensor signals. A requirement is that the sensors are uniformly distributed around the circumference of the drillstring and that the number of sensors is at least two times the number of significant modes. It is demonstrated that the spatial and temporal characteristics of the resolved modes can then be exploited to determine the time of arrival and the angle of direction of the incoming reflected waves.

Relating P‐wave attenuation to permeability

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 20-29 ◽  
Author(s):  
Nabil Akbar ◽  
Jack Dvorkin ◽  
Amos Nur
Keyword(s):  
Pore Radius ◽  
Wave Attenuation ◽  
Three Dimensional ◽  
Low Frequency ◽  
P Wave ◽  
Frequency Wave ◽  
Cylindrical Pore ◽  
Isotropic Elastic Medium ◽  
Plane P Wave ◽  
Attenuation Values

To relate P‐wave attenuation to permeability, we examine a three‐dimensional (3-D) theoretical model of a cylindrical pore filled with viscous fluid and embedded in an infinite isotropic elastic medium. We calculate both attenuation and permeability as functions of the direction of wave propagation. Attenuation estimates are based on the squirt flow mechanism; permeability is calculated using the Kozeny‐Carman relation. We find that in the case when a plane P‐wave propagates perpendicular to the pore orientation [Formula: see text], attenuation is always higher than when a wave propagates parallel to this orientation [Formula: see text]. The ratio of these two attenuation values [Formula: see text] increases with an increasing pore radius and decreasing frequency and saturation. By changing permeability, varying the radius of the pore, we find that the permeability‐attenuation relation is characterized by a peak that shifts toward lower permeabilities as frequency decreases. Therefore, the attenuation of a low‐frequency wave decreases with increasing permeability. We observe a similar trend on relations between attenuation and permeability experimentally obtained on sandstone samples.

scholarly journals Propagation of leaking interface waves

1961 ◽  
Vol 51 (4) ◽  
pp. 527-555
Author(s):  
Robert A. Phinney
Keyword(s):  
P Wave ◽  
Transient Signal ◽  
New Wave ◽  
Wave Problem ◽  
Interface Waves ◽  
Solid Interface ◽  
Interface Wave ◽  
Physical Importance ◽  
Single Integral ◽  
Simple Interface

Abstract With simple generalizations of the method due to Rosenbaum (1961) and Phinney (1961), single integral expressions may be written down for the long range pole contributions to the transient signal in a plane seismic waveguide. This method yields expressions for the leaking, or imperfectly trapped waves, and suffers from no restriction on the number of layers or the existence of coupling to one or two half-spaces. When it is applied to the simple interface wave problem of two halfspaces in contact, closed form expressions are obtained describing the propagation of pulses along the interface due to lower sheet poles. The theory is applied to the Lamb problem, the liquid/solid interface, and the solid/solid interface problems. The leaking wave generalizations of the Rayleigh and Stoneley waves are found and a new wave, coupled to the P-wave, is demonstrated. The physical importance of leaking interface pulses is shown to be in their coupling to the normal or leaking oscillations of layered structures.

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